Math 170 Review
Ch. 11 Conics
1) Determine the conic, and then put into standard form and sketch
x 2 + 4y 2 − 6x + 16y + 21 = 0
2) Sketch the parabola, state the vertex, focus and equation of the directrix x 2 = −8y
(x − 1)2 (y + 3)2
3) Sketch the hyperbola
−
= 1 State the vertices and foci.
9
16
4) Obtain the equation of the parabola with vertex (2,-3) and focus (2,-4)
5) Find the equation of the ellipse with Foci (±3, 0) and vertices (±5, 0)
6) Graph the hyperbola: 9 y 2 − 16 x 2 = 144 state the vertices, foci and equations of the
asymptotes
Answers:
1) Ellipse.
( x − 3)2 ( y + 2)2
+
=1
4
1
2) Parabola faces down, vertex at (0,0) foci at (0,-2) directrix y = 2
3) Hyperbola faces left/right. Vertices (4,-3) and (-2,-3), foci (6,-3) and (-4,-3)
4) ( x − 2)2 = −4( y + 3)
5)
x2 y 2
+
=1
25 16
6) Hyperbola faces up/down. Vertices at (0,4) and (0,-4) Foci at (0,5) and (0,-5)
4
Asymptotes at y = ± x
3